Question

the breadth of a rectangle is two thirds of its length. if the perimeter of the rectangle is 135 cm find the dimensions of the rectangle.​

Answer 1

$Let \: the \: length \: of \: the \: rectangle \: be \: x \: cm \\ then \: its \: breadth = \frac{2x}{3} \: cm \\ \\ perimeter = 2(x + \frac{2x}{3})cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: perimeter \: of \: rectangle = 2(length + breadth) \\ according \: to \: the \: question\\ 2(x + \frac{2x}{3})cm = 135cm \\ \\ \\ 2x + \frac{4x}{3} = 135cm \\ \frac{6x + 4x}{3 } = 135 \\ \\ \frac{10x}{3} = 135 \\ 10x = 135 \times 3 \\ 10x = 405 \\ \\ x <strong><em><u>=</u></em></strong> \frac{405}{10} = 40.5 \\ \\ length = x \: cm = 40.5 \: cm \\ and \: breadth = \frac{2x}{3} cm = \frac{2}{3} \times 40.5cm = 27cm \\ hence, \: the \: dimensions \: of \: the \: rectangle \: are \: 40.5cm \: and \: 27cm.$

Answer 2

$\bf{\huge{\underline{\huge{\boxed{\sf{\blue{Answer:}}}}}}}$

$\bf{\underline{\red{\sf{Given:}}}}$

• The breadth of a rectangle is two thirds of its length.
• The perimeter of the rectangle is 135 cm

$\bf{\underline{\red{\sf{To\:find\::}}}}$

• Length of the rectangle
• Breadth of the rectangle

$\bf{\underline{\red{\sf{Solution:}}}}$

Let the length of the rectangle be x cm

As per first condition :-

• The breadth of a rectangle is two thirds of its length

Breadth = $\large\sf\frac{2}{3}$ x

Perimeter of a rectangle is calculated using the formula,

$\bf{\large{\underline{\boxed{\sf{\purple{Perimeter\:of\:rectangle \:=\:2\:(\:l\:+\:b\:}}}}}}$

Plug in the values in the above formula,

=> 135 = 2 ( x + $\large\sf\frac{2}{3}$ x )

=> 135 = 2 ( x + $\large\sf\frac{2x}{3}$ )

=> 135 = 2 ( $\large\sf\frac{2x\:+\:3x}{3}$ )

=> 135 = 2 ( $\large\sf\frac{5x}{3}$ )

=> 135 = 2 × $\large\sf\frac{5x}{3}$

=> 135 = $\large\sf\frac{10x}{3}$

=> 135 × 3 = 10x

=> 405 = 10x

=> $\large\sf\frac{405}{10}$ = x

=> 40.5 = x

Length of the rectangle = x = 40.5 cm

Breadth of the rectangle = $\large\sf\frac{2}{3}$ × 40.5 = $\large\sf\frac{81}{3}$

Breadth of the rectangle = 27 cm